Elastic and transition form factors of light pseudoscalar mesons from QCD sum rules

We revisit F _π(Q ²) and F _Pγ(Q ²), P = π, η, η′, making use of the local-duality (LD) version of QCD sum rules. We give arguments that the LD sum rule provides reliable predictions for these form factors at Q ² ≥ 5–6 GeV², the accuracy of the method increasing with Q ² in this region. For the pion elastic form factor, the well-measured data at small Q ² give a hint that the LD limit may be reached already at relatively low values of momentum transfers, Q ² ≈ 4–8 GeV²; we therefore conclude that large deviations from LD in the region Q ² = 20–50 GeV² seem very unlikely. The data on the (η, η′) → γγ* form factors meet the expectations from the LD model. However, the BaBar results for the π ⁰ → γγ* form factor imply a violation of LD growing with Q ² even at Q ² ≈ 40 GeV², at odds with the η, η′ case and with the general properties expected for the LD sum rule.     

Relations between the electroexcitation of nucleon resonances and the deep inelastic continuum for proton and deuteron targets

New data of the electroexcitation cross section on protons and deuterons in the resonance region are compared with the results in the deep inelastic region for four-momentum transfers q² ? 1.5 (GeV/c)². The Bloom-Gilman sum rule is shown to hold for q² ? 1.2 (GeV/c) while the Rittenberg-Rubinstein sum rule is saturated for q² ? 0.4 (GeV/c)². It is shown that the sum rules do not saturate in a local way.     

Correlation function for topological charge densities within the instanton model in QCD

The QCD sum rule for the correlation of topological charge densities χ(Q ²) and for the longitudinal part of the correlation function for singlet axial currents (the latter is related to the former) is considered within the instanton model. The constant f _η′ of η′-meson coupling to the singlet axial current is determined. Its value appears to be in good agreement with that determined recently from the relation between the proton-spin fraction Σ carried by u, d, and s quarks and the derivative of the QCD topological susceptibility χ′(0). On the basis of the same sum rule, the η-η′ mixing angle θ₈ is found within the model employing two mixing angles. The value of θ₈ coincides with that in effective chiral theory. The correlation function for topological charge densities χ(Q ²) at large Q ² is calculated. It is shown that the Q ² dependence at high Q ² matches well with that at low Q ², the latter being determined by the known values χ′(0) and by the contributions of the π and η mesons.     

On the kinematics of (e, e′p) reactions

The problem of interpreting experimental data on quasielastic electron scattering on nuclei in A(e, e′p)(A?1) reactions is considered. It is shown that the existing discrepancies in experimental data on the reaction ⁴He(e, e′p)T are associated with the fact that the residual-nucleus momentum p _m as determined from the law of energy-momentum conservation cannot be treated as that which is equal to the momentum p of the primary intranuclear nucleon. Under the assumption that the momentum transferred from the electron to the intranuclear nucleon is redistributed during the divergence of the products of the (e, e′p) reaction in question, the method for extracting p is modified by introducing a kinematical correction, whereby the situation is considerably improved. For a first approximation, the correction can be evaluated on the basis of data on A(e, e′) inclusive reactions. The argument behind this evaluation is illustrated by considering the example of the reaction ⁴He(e, e′p)T.     

Isoscalar quadrupole giant resonance in208Pb: A statistical analysis of high-resolution inelastic electron scattering spectra

The fine structure observed in high resolution inelastic electron scattering spectra for²⁰⁸Pb in the excitation energy range of the isoscalar giant quadrupole resonance has been analysed with a fluctuation analysis technique. The obtained density of levels as a function of excitation energyE _x has then been used as a constraint for the shape and magnitude of the (radiative) background subtracted spectra subjected to a multipole decomposition. The derivedE2 strength in the region 8.0≦E _x≦11.5 MeV exhausts (50 _?7 ⁺¹⁵ % of the energy weighted sum rule. TheE2 strength found is considerably larger than previously estimated from the same spectra and it is now both in shape and magnitude in good agreement with results from a recent²⁰⁸Pb(e, e′n) coincidence experiment.     

Infrared renormalons and the relations between the Gross-Llewellyn Smith and the Bjorken polarized and unpolarized sum rules

It is demonstrated that the infrared renormalon calculus indicates that the QCD theoretical expressions for the Gross-Llewellyn Smith sum rule and for the Bjorken polarized and unpolarized ones contain an identical negative twist-4 1/Q² correction. This observation is supported by the consideration of the results of calculations of the corresponding twist-4 matrix elements. Together with the indication of the similarity of the perturbative QCD contributions to these three sum rules, this observation leads to simple new theoretical relations between the Gross-Llewellyn Smith and Bjorken polarized and unpolarized sum rules in the energy region Q² ≥ 1 GeV². The validity of this relation is checked using concrete experimental data for the Gross-Llewellyn Smith and Bjorken polarized sum rules.     

(e, 2e) spectroscopy of N2—valence momentum distributions and configuration interaction

The noncoplanar symmetric (e, 2e) reaction has been applied to N₂ at 1200, 600 and 400 eV. Separation energy spectra are obtained in the valence region, the observed structure extending to above 60 eV. Electron momentum profiles are measured at a number of separation energies. They agree very well with the momentum distributions for valence orbitals given by SCF calculations. Considerable configuration interaction structure is observed, being primarily due to configuration interaction in the 2σ_g hole state. At 1200 eV the spectroscopic sum rule is satisfied within experimental error, confirming the validity of the analysis.     

Photoelectron spectra and sum rule consideration: Effect of chlorine substitution on ionization energies for chloroethanes,chloroacetaldehydes and chloroacetyl chlorides

He(I) photoelectron spectra are reported for various series of chlorine-substituted compounds: (a) CH₃CH_3?mCl_m, (b) CH_3?mCl_mCCl₃, (c) CH_3?mCl_mCHO and (d) CH_3?mCl_mCOCl, where m = 1, 2 and 3. In each series it is shown that the total sum of vertical ionization energies over all p-type localized molecular orbitals (LO's) has an excellent linear relationship to the number of substituted chlorine atoms. The differences in the total orbital energy sum by successive chlorine substitutions are found to be 26.7 eV for series a and b and 27.2 eV for series c and d, yielding the corresponding experimental σ_CCl, energies useful for sum rule considerations. The photoelectron spectra of the chloro compounds studied are interpreted with the help of the sum rule as well as CNDO/2 calculations. Orbital correlation diagrams have been constructed for these compounds.     

Electronic spectra and structure of the hydrogen halides: Characterization of the electronic structures of HBr and DBr lying between 79 500 and 83 900 cm−1 above X1Σ+

The high-resolution absorption spectra of HBr and DBr were reinvestigated in the 1258-Å (79 500 cm^?1) to 1192-Å (83 900 cm^?1) region. This spectral region was found to contain bands attributable to (1) V¹Σ⁺-X¹Σ⁺(v′ - 0) with v′ > 0, (2) (v′ - 0) transitions with v′ > 0 from X¹Σ⁺(v″ = 0) to states associated with the (σ²π³)cπ and (σ²π³)cσ configurations, and (3) (v′ - 0) transitions with $\text{v′ ≧ 0}$ from X¹Σ⁺(v″ = 0) to states associated with the previously unreported configurations (σ²π³)dσ, dπ, aδ, eσ, and fσ.     

QCD analysis of the Bjorken sum rule revisited

We present extended analysis of the polarized Bjorken sum rule using the four-loop expression for the coefficient function C _Bj(α_s) available now and the recent low Q ²-data from the Jefferson Lab and COMPASS experiments. We demonstrate that the perturbative series for the function C _Bj gives a hint to its asymptotic nature manifesting itself in the region Q ² ? 1 GeV². It is confirmed by the considered integral model for the perturbative QCD correction. We analyze values of higher-twist terms extracted from the mentioned data and discuss the interplay between higher orders perturbative and higher-twist contributions. We extend our consideration to the Gross-Llewellyn Smith sum rule and investigate the relation between higher twist coefficients in these two sum rules.     

Sum rules in QCD for g ηΛΛ and g πΛΣ

New relations between the Borel QCD sum rules for the strong couplings of the Σ⁰ and Λ hyperons are derived. It is shown that, using the sum rules for g _MΣΣ, M = π ⁰, η, as a starting point, one can readily obtain the corresponding sum rules for the coupling constants g _ηΛΛ and g _πΛΣ ⁰. The values of these constants are calculated in a specific parameter region.     

s- and p-wave neutron spectroscopy Xc. Intermediate structure: 88Sr

Neutron total cross section measurements of natural Sr were made from 50–875 keV using a high resolution proton beam and the ⁷Li(p, n) reaction as a neutron source. These data were analyzed with the help of an R-Matrix code to extract resonance (energies and other) parameters up to about 850 keV. 2p-1h and particle-vibration doorway interpretation of the s-, p- and d-wave resonances is attempted in terms of the sum rule Σγ_n² = γ_d². Predictions based on both of these models agree with the experimental results. As expected the p-wave resonances are stronger than either s- and d-wave structure. Theory accounts for the p-wave strength remarkably well. Possible location of the p-wave s.p. resonance is reproduced with a real potential and its damping due to the imaginary potential is calculated.More fragmentation of the strong p-wave doorways is observed than was expected for a compound nucleus so near ⁹⁰Zr, but a larger strength function is observed apparently due to the p-wave giant resonance.     

Electronic excitation in phosphorus-containing molecules. II. Inner shell electron energy loss spectra of PF5, OPF3 AND OPCl3

Electron energy loss Spectroscopy has been used to obtain the inner shell excitation spectra of PF₅, OPF₃ and OPCl₃ in the P 2p,2s (L-shell) region as well as in the respective ligand K shell (F 1s, O 1s) and L shell (Cl 2p and 2s) regions. The spectra are compared and contrasted with earlier reported spectra obtained on the trivalent phosphorus compounds (PH₃, PCl₃, PF₃ and P(CH₃)₃). The spectra were obtained using an impact energy of 2.5keV and a scattering angle of about 1°. The spectra reported here are typical of molecules with electronegative ligands in that the discrete portions of the spectra show strong transitions to virtual molecular orbitais. In addition, intense features are observed at or just beyond the ionization edge attributable to transitions to trapped inner well states, while broad features further into the continuum can be ascribed to σ^*(P—L) shape-resonances (L = ligand). This resonance assignment was supported by a comparison with the corresponding spectra for PF₃ and PCl₃.     

Investigation of the reaction mechanism for the four-particle photodisintegration of a carbon nucleus

The four-particle photodisintegration of a carbon nucleus in the reactions ¹²C(γ, p)³H2α and ¹²C(γ, n)³H2α is investigated by a method that employs a diffusion chamber in a magnetic field. It is shown that these reactions proceed according a sequential-type scheme: excited states of ¹¹B and ¹¹C nuclei decay to weakly excited states of ⁸Be, ⁷Li, and ⁷Be nuclei. It is concluded that nucleons are knocked out from the s shell. In the excitation curve for the 2α system in the reaction ¹²C(γ, p)³H2α, a resonance is found between the maxima corresponding to the ground and the first excited state of the ⁸Be nucleus, and this resonance is identified as a ghost anomaly. The branching fractions of the decay modes are determined. The angular distributions of nucleons in the reaction c.m. frame are measured. The energy dependence of the asymmetry coefficient for the angular distributions is obtained. A fast increase in this coefficient is observed in the energy range 38–40 MeV. It is concluded that the asymmetry coefficient depends on the excitation energy of the final nucleus in the region of intermediate photon energies.     

Factorization and the couplings of the vacuum trajectory

The decoupling theorems associated with an isolated factorizable pomeron pole of unit intercept are re-examined. It is found that the coupling of three such poles, Γ(t, t, 0), need not vanish, precisely at the point t = 0. This is demonstrated by summing only over states in the appropriate unitarity sum, and sum rule, which are consistent with the M², s/M² → ∞ limit. The triple-Regge region then makes a constant contribution to σ_total, insteadsb of the ln lns result obtained if the isolated pole is assumed to couple also to states such that s/M² = constant. The physical implications regarding factorization and the pole-cut relationship are discussed. The relationship between higher order optical theorems (Mueller discontinuities) and particular terms in the unitarity sum for the two → two absorptive part A₂₂ is exploited. Consistent contributions to the triple-Regge region contribute constant vertex corrections to pure pole behaviour in A₂₂. There is no cut contribution and the magnitude of the vertex corrections reflects the relative amount of diffractive production. The analysis is extended to multiple fireball production where pure multipole structures emerge. The series naturally terminates if the diffractive component is sufficiently small. The implications for the behaviour of the total cross section at machine energies are discussed.     

Relaxationsphänomene in Mössbauerspektren von Magnetisierten paramagnetischen Substanzen. I [(Fe x,Al1-x )NH4(SO4)2· 12H2O]

The Fe³⁺-spin in alums of type (Fe _x , A1_1-x )NH₄(SO₄)₂ · 12 H₂O interacts (i) with the crystal lattice viaLS-coupling, and (ii) with the spins of the adjacent Fe³⁺-ions via magnetic dipole-dipole interaction. These interactions lead to a time fluctuation of the spin direction, characterized by correlation times τ _c and τ′ _c of increasing order. The times may be deduced from the⁵⁷Fe-Mössbauer spectra of the alums, τ _c from the width, and τ′ _c ≈τ _c from the position of the hyperfine structure lines. The theoretical interpretation of the Mössbauer spectra is relatively simple, when (i) the spin-lattice interaction gets frozen in, and (ii) a strong applied magnetic fieldH _a decouples the spins of the Fe³⁺-ion and the⁵⁷Fe-nucleus. The spectra were taken, therefore, at 4.2 °K and 8 kOe≦H _a ≦ 54 kOe. According to the 1/r ³-dependence of the magnetic dipole-dipole interaction τ _c should be related tox, the Fe-concentration, τ _c ·x≈τ₀=const. Forx≧0.5 our experimental results are in agreement with this rule when τ₀=(1.5±0.5) · 10^?9 s. For an alum withx=0.26, however, the observed spectra cannot be explained in terms of temporal spin fluctuations, at least not in the framework of the models which are available now. Here, presumedly, the electron spins of adjacent Fe³⁺-ions are coupled to more or less isolated and, consequently, relatively stationary spin clusters of various sizes, leading to many time independent internal magnetic fields. A treatment of this proposal is in preparation.     

Barrier to internal rotation of the silyl group in cyclopropylsilane from combination band spectra

Combination band spectra arising in the region 2000–2300 cm^?1 of cyclopropylsilane can be attributed to the sum and difference bands of the internal rotation with an SiH stretching mode. Analysis of these spectra leads to a potential function for the internal rotation V(cm^?1) = 693.92(1 ? cos 3φ) ? 10.28(1 ? cos 6φ), where φ is the angle of internal rotation. The barrier to internal rotation is thus 1.98 kcal/mole.     

The RPA nuclear continuum in16O(e,e′) reactions at low momentum transfer decay on (e,e′p) and (e,e′n) reaction channels

A theoretical investigation has been performed of¹⁶O(e, e′) and¹⁶O(e, e′x) reactions at low momentum transfer in the frame of a self-consistent HF and RPA theory with a SK3 interaction. Nuclear responses and their multipole components have been calculated in the whole energy-range for the two electron kinematicsi) ? _i =67 MeV and θ=40°,ii) ? _i =130 MeV and θ=50°. The microscopic structure of HF and RPA resonating states in the energy continuum has been inferred from the calculation. Decay properties in the reaction channels (e, e′p) and (e, e′n) have been discussed in the two cases of a semidirect and a knockout reaction process.     

Spin-dipole excitations of6Li in charged pion photoproduction

In the framework of bound shell model we have calculated the photoproduction of charged pions on⁶Li when spin-isospin dipole resonance is excited. It is shown that the transition strength concentrates in several energy regions. Such a gross-structure of the excitation spectrum is governed by the configurational splitting of the resonance. The excitation spectrum in⁶Li(γ, τ)-reaction is compared with the⁶Li(τ, γ), (e, e′) and (n, p)-reaction spectra where spin-isospin transitions are dominating too.     

Pigmy and giant dipole states in stable and unstable oxygen isotopes

We have studied dipole states of oxygen isotopes in large scale shell model calculations. The calculated photoreaction cross sections in ¹⁶O, ¹⁷O and ¹⁸O give reasonable agreement with experimental observations both in the low energy region below ?ω=15 MeV and in the high energy giant resonance region (15 MeV < ?ω ≤ 30 MeV). We found that the transition strength below dipole giant resonance (?ω ≤ 15 MeV) exhausts about 10% of the classical Thomas-Reiche-Kuhn sum rule and more than 40% of the cluster sum rule in heavier oxygen isotopes than ¹⁷O. The predicted Pigmy strengths in ²⁰O and ²²O are also confirmed by recent Coulomb excitation experiment at GSI.